Take-off in Levora
Entries stay tied to their item, and the formula stays visible.
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Quantities to REB 23.003
Five formulas from the official catalogue, each with the calculation visible. Result and steps can be taken away as CSV – as an annex to the take-off.
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Choose a formula
German decimal commas are allowed: 1,25 and 1.25 are the same thing.
a · b – area · a · b · H – volume
Without H you get an area, with H a volume. That is how the catalogue puts it: the height is the additional final argument.
a · h ÷ 2 – area · a · h · H ÷ 2 – volume
h is the height within the triangle, H the height of the body above it. Confuse the two and you calculate the wrong thing cleanly.
(a + b) ÷ 2 · h – area · (a + b) ÷ 2 · h · H – volume
a and b are the two parallel sides.
(F1 + F2) ÷ 2 · L – volume between two areas
The cross-section case: two profile areas and the distance between them.
a · h · (H1 + H2 + H3) ÷ 6
The oblique prism with three different edge heights – the normal case for a milled surface of uneven depth.
½ · |Σ (yᵢ − yᵢ₊₁) · (zᵢ + zᵢ₊₁)| – optional · D
The first point must be repeated at the end – the catalogue requires it. Only y and z are used; the x coordinate stays out of it. Negative signs are allowed here, but not in the other four formulas.
Result
This calculator failed its own test cases and has been switched off. Please tell us – a take-off that calculates wrongly only shows up at the audit.
Please enter a number.
Thickness D: please enter a number – or leave the field empty for the area.
Invalid or negative value at
Two numbers expected per line – line
A polygon needs at least three points plus the repetition of the first.
The last point must match the first – otherwise the polygon is not closed.Formula
Calculation
Result
reb-23003-formula
Gauss's area formula
edges
Without JavaScript this tool does not calculate. The expressions are printed beside each formula and can be followed on a pocket calculator.
The calculation runs in the browser. Your measurements are not sent and not stored.
Where the formulas come from
From the Formelkatalog Straßenbau of REB-VB 23.003, 2012 edition, published by the German Federal Highway Research Institute (BASt). The document is freely available; the expressions above are taken from it and not from a summary somewhere on the web. Basing a take-off on an invented formula produces a wrong calculation with an official-sounding number in front of it – and that surfaces at the audit at the latest.
The catalogue holds 36 formulas. Five are here: the ones that cover most cases in road and paving work. More will follow when there is a reason for them – not to fill out a list.
| No. | Formula | Expression |
|---|---|---|
| 1 | Triangle / prism | a · h ÷ 2 · with H: a · h · H ÷ 2 |
| 4 | Rectangle / cuboid | a · b · with H: a · b · H |
| 5 | Trapezoid / trapezoidal prism | (a + b) ÷ 2 · h · with H additionally · H |
| 5c | Volume between two areas | (F1 + F2) ÷ 2 · L |
| 13 | Oblique prism | a · h · (H1 + H2 + H3) ÷ 6 |
| 22 | Polygon from coordinates | Gauss’s area formula, optionally · D |
Two rules from the catalogue that are often missed
The height is the last argument. An area becomes a volume by putting a height H after the values otherwise required. That is why almost every formula here has an optional H field, and why the result then switches from m² to m³. Confuse h and H – the height within the triangle and the height of the body – and you calculate the wrong thing cleanly.
Negative signs are permitted only in certain formulas, namely 21, 22, 23, 25, 26, 27 and 28. Of the five here that is formula 22 alone; in the others the calculator rejects negative values instead of silently processing them.
For the polygon from coordinates: the first point must be repeated at the end, and only y and z are used. An x coordinate is not taken into account. The direction in which you traverse the polygon does not change the result – the absolute value takes care of that.
What this calculator is not
It is not a take-off program. It calculates one formula, shows the steps and outputs both as CSV. What it cannot do: collect entries across several items, assign them to an item in the bill of quantities, carry them forward when a quantity changes, and finally produce an auditable take-off to REB that can be presented to the client.
That chain is the actual work – not the single multiplication. It is the reason Levora exists.
As of 16 August 2026. Source: REB-VB 23.003, Formelkatalog Straßenbau (BASt, PDF) .
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